Limits and Continuity

Limits and Continuity

Limits and Continuity

Limits and Continuity

Limits and Continuity

Limits and Continuity

The concept of the limit is one of the most crucial things to understand in
order to prepare for calculus. A limit is a number that a function approaches
as the independent variable of the function approaches a given value. For
example, given the function f (x) = 3x, you could say, "The limit of f (x) as
x approaches 2 is 6." Symbolically, this is written f (x) = 6. In the following sections, we will more carefully define a limit, as well
as give examples of limits of functions to help clarify the concept.

Continuity is another far-reaching concept in calculus. A function can
either be continuous or discontinuous. One easy way to test for the continuity
of a function is to see whether the graph of a function can be traced with a pen
without lifting the pen from the paper. For the math that we are doing in
precalculus and calculus, a conceptual definition of continuity like this one is
probably sufficient, but for higher math, a more technical definition is needed.
Using limits, we'll learn a better and far more precise way of defining
continuity as well. With an understanding of the concepts of limits and
continuity, you are ready for calculus.